On nilpotent Lie algebras of derivations with large center
Let \(\mathbb K\) be a field of characteristic zero and \(A\) an associative commutative \(\mathbb K\)-algebra that is an integral domain. Denote by \(R\) the quotient field of \(A\) and by \(W(A)=R\operatorname{Der} A\) the Lie algebra of derivations on \(R\) that are products of elements of \(R\)...
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| Дата: | 2016 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2016
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/132 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543377549426688 |
|---|---|
| author | Sysak, Kateryna |
| author_facet | Sysak, Kateryna |
| author_sort | Sysak, Kateryna |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-05-11T05:58:23Z |
| description | Let \(\mathbb K\) be a field of characteristic zero and \(A\) an associative commutative \(\mathbb K\)-algebra that is an integral domain. Denote by \(R\) the quotient field of \(A\) and by \(W(A)=R\operatorname{Der} A\) the Lie algebra of derivations on \(R\) that are products of elements of \(R\) and derivations on \(A\). Nilpotent Lie subalgebras of the Lie algebra \(W(A)\) of rank \(n\) over \(R\) with the center of rank \(n-1\) are studied. It is proved that such a Lie algebra \(L\) is isomorphic to a subalgebra of the Lie algebra \(u_n(F)\) of triangular polynomial derivations where \(F\) is the field of constants for \(L\). |
| first_indexed | 2025-12-02T15:42:03Z |
| format | Article |
| id | admjournalluguniveduua-article-132 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:42:03Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-1322016-05-11T05:58:23Z On nilpotent Lie algebras of derivations with large center Sysak, Kateryna derivation, Lie algebra, nilpotent Lie subalgebra, triangular derivation, polynomial algebra. Primary 17B66; Secondary 17B30, 13N15. Let \(\mathbb K\) be a field of characteristic zero and \(A\) an associative commutative \(\mathbb K\)-algebra that is an integral domain. Denote by \(R\) the quotient field of \(A\) and by \(W(A)=R\operatorname{Der} A\) the Lie algebra of derivations on \(R\) that are products of elements of \(R\) and derivations on \(A\). Nilpotent Lie subalgebras of the Lie algebra \(W(A)\) of rank \(n\) over \(R\) with the center of rank \(n-1\) are studied. It is proved that such a Lie algebra \(L\) is isomorphic to a subalgebra of the Lie algebra \(u_n(F)\) of triangular polynomial derivations where \(F\) is the field of constants for \(L\). Lugansk National Taras Shevchenko University 2016-05-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/132 Algebra and Discrete Mathematics; Vol 21, No 1 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/132/pdf Copyright (c) 2016 Algebra and Discrete Mathematics |
| spellingShingle | derivation Lie algebra nilpotent Lie subalgebra triangular derivation polynomial algebra. Primary 17B66; Secondary 17B30 13N15. Sysak, Kateryna On nilpotent Lie algebras of derivations with large center |
| title | On nilpotent Lie algebras of derivations with large center |
| title_full | On nilpotent Lie algebras of derivations with large center |
| title_fullStr | On nilpotent Lie algebras of derivations with large center |
| title_full_unstemmed | On nilpotent Lie algebras of derivations with large center |
| title_short | On nilpotent Lie algebras of derivations with large center |
| title_sort | on nilpotent lie algebras of derivations with large center |
| topic | derivation Lie algebra nilpotent Lie subalgebra triangular derivation polynomial algebra. Primary 17B66; Secondary 17B30 13N15. |
| topic_facet | derivation Lie algebra nilpotent Lie subalgebra triangular derivation polynomial algebra. Primary 17B66; Secondary 17B30 13N15. |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/132 |
| work_keys_str_mv | AT sysakkateryna onnilpotentliealgebrasofderivationswithlargecenter |